[CAUT] professor tuning variables

[Dennis Johnson]

Hi Scott-
A proportionally beating triad is a triad in which 2 or more of the
contained intervals are beating at speeds proportional to each other. For
example,  inside a pure fifth the root position minor triad (m3 and M3)
should both beat at exactly the same speeds. To be technical, there can be
an inharmonic difference between this 6:4 fifth and usual 3:2 fifth most
commonly used for testing the purity, but that is a decision for the tuner.

My use of the word symmetry in this case refers to the relationship between
sharp and flat keys. For example, in a theoretically perfect Thomas Young
temperament the circle has symmetry because corresponding sharp and flat
keys are exactly the size across the circle. FA=GB, BbD=BF#,
EbG=AC#,AbC=EG#, DbF=BD#, and GbBb=F#A#.  This particular temperament, and
theoretical variations of it, are discussed in detail in Jorgensen's big red
Tuning book.

Hope that helps,

Dennis Johnson
_____________

On Mon, Mar 9, 2009 at 5:04 AM, Scott Jackson <scottwaynejackson at hotmail.com
> wrote:

>  Dennis, or anyone,
> Can you elaborate on "symmetry or proportionally beating triads". I don't
> think that it is a phrase that I have heard used before.
> Thanks,
>
> Scott Jackson
>
>
> ----- Original Message -----
> *From:* Dennis Johnson <johnsond at stolaf.edu>
> *To:* caut at ptg.org
> *Sent:* Thursday, February 26, 2009 2:53 AM
> *Subject:* Re: [CAUT] professor tuning variables (David Love)
>
>
> Shifting particular notes by 1/2 cent either way to hone in symmetry or
> proportionally beating triads are the aesthetic judgements that make me
> smile on the job.
>
> Dennis Johnson
> St. Olaf College
>
>
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